Structural Reliability: Approaches from Perspectives of Statistical Moments

656 Pages·2021·25.972 MB·English

by  Yan-Gang Zhao, Zhao-Hui Lu

Structural Reliability

Structural Reliability
Approaches from Perspectives of Statistical Moments
Yan-Gang Zhao and Zhao-Hui Lu
Thiseditionfirstpublished2021
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LibraryofCongressCataloging-in-PublicationData
Names:Zhao,Yan-Gang,author.|Lu,Zhao-Hui,author.
Title:Structuralreliability:approachesfromperspectivesofstatistical
moments/Yan-GangZhaoandZhao-HuiLu.
Description:Hoboken,NJ,USA:Wiley-Blackwell,2021.|Includes
bibliographicalreferencesandindex.
Identifiers:LCCN2020041116(print)|LCCN2020041117(ebook)|ISBN
9781119620815(cloth)|ISBN9781119620693(adobepdf)|ISBN
9781119620747(epub)
Subjects:LCSH:Structuralengineering–Statisticalmethods.|Reliability
(Engineering)–Mathematics.|Momentsmethod(Statistics)
Classification:LCCTA650.Z532021 (print)|LCCTA650 (ebook)|DDC
624.1–dc23
LCrecordavailableathttps://lccn.loc.gov/2020041116
LCebookrecordavailableathttps://lccn.loc.gov/2020041117
CoverDesign:Wiley
CoverImage:©LIUKAIYOU/GettyImages
10 9 8 7 6 5 4 3 2 1
v
Contents
Preface xi
Acknowledgements xv
1 MeasuresofStructuralSafety 1
1.1 Introduction 1
1.2 UncertaintiesinStructuralDesign 1
1.2.1 UncertaintiesinthePropertiesofStructuresandTheirEnvironment 1
1.2.2 SourcesandTypesofUncertainties 4
1.2.3 TreatmentofUncertainties 5
1.2.4 DesignandDecisionMakingwithUncertainties 9
1.3 DeterministicMeasuresofSafety 9
1.4 ProbabilisticMeasureofSafety 10
1.5 Summary 10
2 FundamentalsofStructuralReliabilityTheory 11
2.1 TheFundamentalCase 11
2.2 PerformanceFunctionandProbabilityofFailure 16
2.2.1 PerformanceFunction 16
2.2.2 ProbabilityofFailure 17
2.2.3 ReliabilityIndex 19
2.3 MonteCarloSimulation 24
2.3.1 FormulationoftheProbabilityofFailure 24
2.3.2 GenerationofRandomNumbers 25
2.3.3 DirectSamplingforStructuralReliabilityEvaluation 28
2.4 ABriefReviewonStructuralReliabilityTheory 33
2.5 Summary 35
3 MomentEvaluationforPerformanceFunctions 37
3.1 Introduction 37
3.2 MomentComputationforsomeSimpleFunctions 39
3.2.1 MomentComputationforLinearSumofRandomVariables 39
3.2.2 MomentComputationforProductsofRandomVariables 42
vi Contents
3.2.3 MomentComputationforPowerofaLognormallyDistributedRandom
Variable 45
3.2.4 MomentComputationforPowerofanArbitrarilyDistributedRandom
Variable 50
3.2.5 MomentComputationforReciprocalofanArbitraryDistributedRandom
Variable 52
3.3 PointEstimatesforaFunctionwithOneRandomVariable 53
3.3.1 Rosenblueth’sTwo-PointEstimate 53
3.3.2 Gorman’sThree-PointEstimate 55
3.4 PointEstimatesinStandardisedNormalSpace 60
3.4.1 FormulaeofMomentofFunctionswithSingleRandomVariable 60
3.4.2 Two-andThree-PointEstimatesintheStandardNormalSpace 63
3.4.3 Five-PointEstimateinStandardNormalSpace 64
3.4.4 Seven-PointEstimateinStandardNormalSpace 65
3.4.5 GeneralExpressionofEstimatingPointsandTheirCorrespondingWeights 68
3.4.6 AccuracyofthePointEstimate 70
3.5 PointEstimatesforaFunctionofMultipleVariables 76
3.5.1 GeneralExpressionofPointEstimatesforaFunctionofnVariables 76
3.5.2 ApproximatePointEstimatesforaFunctionofnVariables 78
3.5.3 DimensionReductionIntegration 83
3.6 PointEstimatesforaFunctionofCorrelatedRandomVariables 89
3.7 HybridDimension-ReductionBasedPointEstimateMethod 94
3.8 Summary 96
4 DirectMethodsofMoment 99
4.1 BasicConceptofMethodsofMoment 99
4.1.1 IntegralExpressionofProbabilityofFailure 99
4.1.2 TheSecond-MomentMethod 100
4.1.3 GeneralExpressionsforMethodsofMoment 102
4.2 Third-MomentReliabilityMethod 104
4.2.1 GeneralFormulationoftheThird-MomentReliabilityIndex 104
4.2.2 Third-MomentReliabilityIndices 106
4.2.3 EmpiricalApplicableRangeofThird-MomentMethod 110
4.2.4 SimplificationofThird-MomentReliabilityIndex 113
4.2.5 ApplicableRangeoftheSecond-MomentMethod 117
4.3 Fourth-MomentReliabilityMethod 122
4.3.1 GeneralFormulationoftheFourth-MomentReliabilityIndex 122
4.3.2 Fourth-MomentReliabilityIndexontheBasisofthePearsonSystem 124
4.3.3 Fourth-MomentReliabilityIndexBasedonThird-OrderPolynomial
Transformation 127
4.3.4 ApplicableRangeofFourth-MomentMethod 130
4.3.5 SimplificationofFourth-MomentReliabilityIndex 136
4.4 Summary 138
Contents vii
5 MethodsofMomentBasedonFirst-andSecond-OrderTransformation 139
5.1 Introduction 139
5.2 First-OrderReliabilityMethod 139
5.2.1 TheHasofer-LindReliabilityIndex 139
5.2.2 First-OrderReliabilityMethod 141
5.2.3 NumericalSolutionforFORM 147
5.2.4 TheWeaknessofFORM 153
5.3 Second-OrderReliabilityMethod 156
5.3.1 NecessityofSecond-OrderReliabilityMethod 156
5.3.2 Second-OrderApproximationofthePerformanceFunction 157
5.3.3 FailureProbabilityforSecond-OrderPerformanceFunction 170
5.3.4 MethodsofMomentforSecond-OrderApproximation 175
5.3.5 ApplicableRangeofFORM 187
5.4 Summary 191
6 StructuralReliabilityAssessmentBasedontheInformationofMomentsof
RandomVariables 193
6.1 Introduction 193
6.2 DirectMethodsofMomentwithoutUsingProbabilityDistribution 195
6.2.1 Second-MomentFormulation 195
6.2.2 Third-MomentFormulation 196
6.2.3 Fourth-MomentFormulation 196
6.3 First-OrderSecond-MomentMethod 197
6.4 First-OrderThird-MomentMethod 203
6.4.1 First-OrderThird-MomentMethodinReducedSpace 203
6.4.2 First-OrderThird-MomentMethodinThird-MomentPseudoStandardNormal
Space 204
6.5 First-OrderFourth-MomentMethod 219
6.5.1 First-OrderFourth-MomentMethodinReducedSpace 219
6.5.2 First-OrderFourth-MomentMethodinFourth-MomentPseudoStandardNormal
Space 220
6.6 MonteCarloSimulationUsingStatisticalMomentsofRandomVariables 233
6.7 SubsetSimulationUsingStatisticalMomentsofRandomVariables 246
6.8 Summary 252
7 TransformationofNon-NormalVariablestoIndependentNormalVariables 253
7.1 Introduction 253
7.2 TheNormalTransformationforaSingleRandomVariable 253
7.3 TheNormalTransformationforCorrelatedRandomVariables 254
7.3.1 RosenblattTransformation 254
7.3.2 NatafTransformation 255
7.4 PseudoNormalTransformationsforaSingleRandomVariable 265
7.4.1 ConceptofPseudoNormalTransformation 265
viii Contents
7.4.2 Third-MomentPseudoNormalTransformation 267
7.4.3 Fourth-MomentPseudoNormalTransformation 274
7.5 PseudoNormalTransformationsofCorrelatedRandomVariables 293
7.5.1 Introduction 293
7.5.2 Third-MomentPseudoNormalTransformationforCorrelatedRandom
Variables 295
7.5.3 Fourth-MomentPseudoNormalTransformationforCorrelatedRandom
Variables 298
7.6 Summary 306
8 SystemReliabilityAssessmentbytheMethodsofMoment 307
8.1 Introduction 307
8.2 BasicConceptsofSystemReliability 307
8.2.1 MultipleFailureModes 307
8.2.2 SeriesSystems 308
8.2.3 ParallelSystems 311
8.3 SystemReliabilityBounds 318
8.3.1 Uni-ModalBounds 318
8.3.2 Bi-ModalBounds 320
8.3.3 CorrelationBetweenaPairofFailureModes 322
8.3.4 BoundEstimationoftheJointFailureProbabilityofaPairofFailureModes 324
8.3.5 PointEstimationoftheJointFailureProbabilityofaPairofFailureModes 327
8.4 MomentApproachforSystemReliability 338
8.4.1 PerformanceFunctionforaSystem 339
8.4.2 MethodsofMomentforSystemReliability 342
8.5 SystemReliabilityAssessmentofDuctileFrameStructuresUsingMethodsof
Moment 352
8.5.1 ChallengesonSystemReliabilityofDuctileFrames 352
8.5.2 PerformanceFunctionIndependentofFailureModes 353
8.5.3 LimitAnalysis 355
8.5.4 MethodsofMomentforSystemReliabilityofDuctileFrames 356
8.6 Summary 364
9 DeterminationofLoadandResistanceFactorsbyMethodsofMoment 365
9.1 Introduction 365
9.2 LoadandResistanceFactors 366
9.2.1 BasicConcept 366
9.2.2 DeterminationofLRFsbySecond-MomentMethod 366
9.2.3 DeterminationofLRFsUnderLognormalAssumption 369
9.2.4 DeterminationofLRFsUsingFORM 370
9.2.5 AnApproximateMethodfortheDeterminationofLRFs 378
9.3 LoadandResistanceFactorsbyThird-MomentMethod 380
9.3.1 DeterminationofLRFsUsingThird-MomentMethod 380